On the universal cover and the fundamental group of an $RC{D}^{\ast }(K,N)$-space

Abstract

The main goal of the paper is to prove the existence of the universal cover for $RC{D}^{\ast }(K,N)$-spaces. This generalizes earlier work of C. Sormani and the second named author on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental group of such spaces. These are the first topological results for $RC{D}^{\ast }(K,N)$-spaces without extra structural-topological assumptions (such as semi-local simple connectedness).

Final version to appear in Journal für die Reine und Angewandte Mathematik

References in corpus (1)

• Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

Cited by in corpus (10)

• Maximal volume entropy rigidity for ${\mathsf{RCD}}^{\ast }(-(N-1),N)$ spaces
• Singular Weyl's law with Ricci curvature bounded below
• An upper bound on the revised first Betti number and a torus stability result for RCD spaces
• On fundamental groups of RCD spaces
• Isometric immersions of RCD$(K,N)$ spaces via heat kernels
• Moduli spaces of compact RCD(0,N)-structures
• The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth
• On manifolds with almost non-negative Ricci curvature and integrally-positive $k^{th}$-scalar curvature
• Margulis Lemma on $\text{RCD}(K,N)$ spaces
• Precompactness of domains with lower Ricci curvature bound under Gromov-Hausdorff topology